The Diffraction of Oblique Surface Waves By a Right Angle Bend
The Diffraction of Oblique Surface Waves By a Right Angle Bend
Samuel Karp
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A)a|.^/3''p^a), . , „, ] (4. 40; J>'f (K?)d| ^1 . 2 Now the explicit expressions for the six coefficients k, R, A, B, B^, and C^ have been obtained in the six equations, (4. 34), (4.^35), (4. 40), (4. 27), (4. 38) and (4. 25) respectively. This observation completes the formal solution of this case. It is of interest to determine the far-zone forms of the radiated field. We first w ite down the asymptotic forms of the functions f and g. (4. 41) f 1 v JtKr ■f ll«^ [^ i(Kr-— ) ^ (4. 42) g ~ e iko.... S' The far- zone forms of \|/ and f are expected to be (4. 43) M (cp) ^ iHcr + ik^. S' VT 18 (k. Hk) ^ = COS4) ^ - - smcp g;: ~ coscp^ . Substituting Egs. (UAl), (k. HS) and (U. U) into Eq. (h. L'^) gives (^•^5) 1^1 = i. Cos cp-a^ y^ ^ [^1 sin ^ cp e + A^sin rcpe Substituting Eqs. {k. K2), {h. K3) and (h. Kk) into Eq. (U. L8) gives (^•^6) ^2= i. Cosc^-a, sl-^r ' ^BpSin f cp e 12, ^^3^, ^^, 12 J ^ Then substituting the above two expressions into Eq. . (^-^O) yields ih. Hl) E = T-r-^ 7 / -^ e -^^ ^' '-/^ ^^-- Lsin |cp +A^sin ^cpe ^ 1 r 2 1| "^^1 ^ iK cos cp -a^ [\-- I ^ -^^2^^- 3 ^^ J rr- KKr-g^-k S')f a \ 2 U -ifl (1+.
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